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Decay of helical and non-helicalmagnetic links and knots
Simon Candelaresi,Axel Brandenburg
and Fabio Del Sordo
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Magnetic helicity
Realizability condition:
Magnetic energy is bound from below by magnetic helicity.
trefoil knot
twisted field
magnetic helicity conservation
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Interlocked flux rings
● Isothermal compressible gas● Viscous medium● Periodic boundaries
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Interlocked flux rings
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Interlocked flux rings
Magnetic helicity rather then actual linking determines the field decay.
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N-foil knots
3-foil 5-foil4-foil 6-foil 7-foil
*
* from Wikipedia, author: Jim.belk
cinquefoil knot
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Magnetic helicity is approximately conserved.
Self-linking is transformed into twisting after reconnection.
N-foil knots
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Slower decay for higher .
N-foil knots
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N-foil knots
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Realizability condition more important for high .
N-foil knots
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IUCAA knotBorromean rings
IUCAA knot and Borromean rings
● Is magnetic helicity sufficient?● Higher order invariants?
IUCAA = The Inter-University Centre for Astronomy and Astrophysics, Pune, India
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Reconnection characteristics
3 rings Twisted ring + interlocked rings
2 twisted rings
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Reconnection characteristics
Conversion of linking into twisting
Ruzmaikin and Akhmetiev (1994)
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Magnetic energy decay
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Conclusions
● Topology can constrain field decay.● Stronger packing for high leads to different decay slopes.● Higher order invariants?
● Non-forced ejection of magnetic field● Isolated helical structures inhibit energy decay● Reconsider realizability condition
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References
Del Sordo et al. 2010
Fabio Del Sordo, Simon Candelaresi, and Axel Brandenburg. Magnetic-field decay of three interlocked flux rings with zero linking number. Phys. Rev. E, 81:036401, Mar 2010.
A. Ruzmaikin and P. Akhmetiev.Topological invariants of magnetic fields, and the effect of reconnections.Phys. Plasmas, vol. 1, pp. 331–336, 1994.
Ruzmaikin and Akhmetiev 1994
Candelaresi and Brandenburg 2011
Simon Candelaresi, and Axel Brandenburg. Decay of helical and non-helical magnetic knots. Phys. Rev. E, accepted.
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Simulations
● mesh point● Isothermal compressible gas● Viscous medium● Periodic boundaries
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Magnetic energy decay
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Linking number
Number of crossingsincreases like
Sign of the crossings for the 4-foil knot
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Helicity vs. energy
Knot is more strongly packed with increasing .
Magnetic energy is closer to its lower limit for high .